Rafail Abramov
Department of Mathematics, Statistics and Computer Science
University of Illinois at Chicago
851 S. Morgan St.
Chicago, IL 60607
E-mail: abramov@math.uic.edu
Phone: (312) 413 7945
Publications
A. Majda, R. Abramov & B. Gershgorin, High skill in low
frequency climate response through fluctuation dissipation
theorems despite structural instability, submitted to
Proceedings of the National Academy of Sciences, 2009.
R. Abramov, Linear response for slow variables of deterministic or
stochastic dynamics with time scale separation, submitted to
Journal of Computational Physics, 2009.
[PDF] (preprint)
R. Abramov, Short-time linear response with reduced-rank
tangent map, accepted to Chinese Annals of Mathematics,
2009.
[PDF] (preprint)
R. Abramov, The multidimensional maximum entropy moment
problem: A review on numerical methods, accepted to
Communications in Mathematical Sciences, 2009.
[PDF] (preprint)
R. Abramov, The multidimensional moment-constrained
maximum entropy problem: A BFGS algorithm with constraint
scaling, Journal of Computational Physics, 2009,
vol. 228, 96—108.
[DOI
link]
R. Abramov & A. Majda, A new algorithm for low
frequency climate response, Journal of the
Atmospheric Sciences, 2009, vol. 66, 286—309.
[DOI link]
R. Abramov & A. Majda, New approximations and tests of
linear fluctuation-response for chaotic nonlinear
forced-dissipative dynamical systems, Journal of
Nonlinear Science, 2008, vol. 18, 303—341.
[PDF]
R. Abramov & A. Majda, Blended response algorithms for
linear fluctuation-dissipation for complex nonlinear dynamical
systems, Nonlinearity, 2007, vol. 20, 2793—2821.
[PDF]
R. Abramov, An improved algorithm for the multidimensional
moment-constrained maximum entropy problem, Journal of
Computational Physics, 2007, vol. 226, 621—644.
[DOI
link]
R. Abramov, A practical computational framework for the
multidimensional moment-constrained maximum entropy
principle, Journal of Computational Physics, 2006,
vol. 211, 198—209.
[DOI
link]
A. Majda, R. Abramov & M. Grote, Information theory
and stochastics for multiscale nonlinear systems, vol. 25
of CRM Monograph Series, Centre de Recherches
Mathématiques, Université de
Montréal. Published by American Mathematical Society,
2005. ISBN 0-8218-3843-1. 141 pp.
[Amazon]
[Barnes
& Noble]
K. Haven, A. Majda & R. Abramov, Quantifying
predictability through information theory: Small sample
estimation in a non-Gaussian framework, Journal of
Computational Physics, 2005, vol. 206, 334—362.
[DOI
link]
R. Abramov, A. Majda & R. Kleeman, Information Theory
and Predictability for Low Frequency Variability, Journal
of Atmospheric Sciences, 2005, vol. 62, no. 1,
65—87.
[PDF]
R. Abramov & A. Majda, Quantifying uncertainty for
non-Gaussian ensembles in complex systems, SIAM Journal
on Scientific Computing, 2003, vol. 26, no. 2,
411—447.
[PDF]
R. Abramov & A. Majda, Discrete approximations with
additional conserved quantities: Deterministic and statistical
behavior, Methods and Applications of Analysis, 2003,
vol. 10, no. 2, 151—190.
[PDF]
R. Abramov & A. Majda, Statistically relevant
conserved quantities for truncated quasi-geostrophic
flow, Proceedings of the National Academy of Sciences, 2003,
vol. 100, no. 7, 3841—3846.
[PDF]
R. Abramov, G. Kovačič & A. Majda, Hamiltonian
structure and statistically relevant conserved quantities for
the truncated Burgers-Hopf equation, Communications in
Pure and Applied Mathematics, 2003, vol. 56,
1—46.
[PDF]
Ph.D. Rensselaer Polytechnic
Institute, Department of
Mathematics, 2002.
Thesis title: Statistically
relevant and irrelevant conserved quantities for the
equilibrium statistical description of the truncated
Burgers-Hopf equation and the equations for barotropic
flow.
[PDF]
Software
The multidimensional moment-constrained maximum entropy algorithm
This page is currently under heavy construction, however the full algorithm library for the i586 platform is there with few examples in C, C++ and FORTRAN (see file maxent_dist.tar.gz). The proper manual is currently lacking.
Teaching
MATH 480 — Applied Differential Equations